How can I display the currently selected settings in a panel?
After playing around with it, I think it would be easier just to add this: 

scene = context.scene
view = scene.view_settings
row.prop(view, "view_transform")


Not only do we get the options we want but we can see which is active.



Alternatively, as brockmann has said, you can use:

layout.prop(view, "view_transform", expand=True)


which would give you this -